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This volume brings together fourteen essays authored by distinguished mathematicians from India, offering a panoramic view of current research directions as well as recent historical developments in mathematics in India. The articles cover diverse topics—number theory, operator algebra, operator theory, harmonic analysis, quantum learning, noncommutative geometry and random matrices—showcasing the breadth and depth of contemporary mathematical research. The book provides a vivid snapshot of mathematical thought as it evolves today, connecting tradition with innovation and offering both insight and inspiration to the next generation of mathematicians.
The volume opens with an illuminating essay by M. S. Raghunathan, “Some Highlights of Indian Contributions to Mathematics in the 20th Century”, a comprehensive historical account of post-Independence mathematical research in India that will inspire young readers and scholars alike. A special inclusion is the research article “Symmetric Products and Moduli Spaces of Vector Bundles on Curves” by Kyoung-Seog Lee and the late M. S. Narasimhan, completed shortly before Narasimhan’s passing in 2021. This paper, which has already attracted wide attention in the research community, stands as a fitting tribute to his enduring influence in algebraic geometry.
List of contents
Some Highlights of Indian Contributions to Mathematics in the 20th Century.- Convex Analysis-Statistical Theory of Decisions and of Machine Learning Classical and Quantum.- Symmetric Products and Moduli Spaces of Vector Bundles of Curves.- Classification of C algebras, Spaces of Operators and Function Spaces using the Geometry of Banach Spaces.- Contribution to Random Matrices by Indian statisticians and Probabilists: A Brief Survey.- Normalisation of Scores, Multiple Choice Questions, over Multi-phase Tests.- Recent Developments in Analytic Number Theory.- A brief history of Noncommutative Geometry in India.- A Compendium of Research in Operator Theory and Operator Algebra.- Hardy-Hilbert Spaces for General Domains.- The Geometry of Bruhat-Tits Groups.- A Survey of Fourier Analysis on Riemannian Symmetric Spaces: Contribution of Indian Mathematicians (2000–2025).- Positivity and Negativity Preservers under the Entrywise Calculus.- A Survey and a Result on Inhomogeneous Quadratic Forms.
About the author
Gadadhar Misra
is Visiting Professor in the Department of Mathematics, the Indian Institute of Technology Gandhinagar, Gujarat, India. Earlier, he has been Chairman and Professor in the Department of Mathematics, the Indian Institute of Science (IISc), Bengaluru, Karnataka, India. He was also Head of the Indian Statistical Institute, Bangalore, Karnataka, India. A distinguished mathematician, a brilliant teacher and an active researcher, he held several key positions: member of the National Board of Higher Mathematics; Co-convener of the KVPY and the Indian Academy of Sciences (2007–2009). He is the Fellow of the Indian Academy of Sciences, the Indian National Science Academy, the National Academy of Sciences and a recipient of J.C. Fellowship. His research interests lie in operator theory, functional analysis and Hilbert modules. He has been contributing significantly to promoting collaborative research and strengthening mathematical education in India.
After completing his master’s from Sambalpur University, he pursued his Ph.D. under the supervision of Prof. Ronald G. Douglas at Stony Brook, USA. His dissertation on “Curvature Inequalities and External Properties of Bundle Shifts” laid the foundation of a life wedded to academics and high-end research. He had the privilege of working jointly with eminent scientists like J. Jiang and others which resulted in new findings with regard to homogeneous operators, Hilbert modules and Geometric invariants for quotient modules. He has published several papers in national and international journals besides guiding scholars leading to their PhD degrees. He received several prestigious awards including the Shanti Swarup Bhatnagar Award for outstanding work in 2001. In humble recognition of his excellent research and academic credentials, the Odisha Bigyan Academy conferred on him the Biju Patnaik Award for Scientific Excellence for the year 2013.
Summary
This volume brings together fourteen essays authored by distinguished mathematicians from India, offering a panoramic view of current research directions as well as recent historical developments in mathematics in India. The articles cover diverse topics—number theory, operator algebra, operator theory, harmonic analysis, quantum learning, noncommutative geometry and random matrices—showcasing the breadth and depth of contemporary mathematical research. The book provides a vivid snapshot of mathematical thought as it evolves today, connecting tradition with innovation and offering both insight and inspiration to the next generation of mathematicians.
The volume opens with an illuminating essay by M. S. Raghunathan, “Some Highlights of Indian Contributions to Mathematics in the 20th Century”, a comprehensive historical account of post-Independence mathematical research in India that will inspire young readers and scholars alike. A special inclusion is the research article “Symmetric Products and Moduli Spaces of Vector Bundles on Curves” by Kyoung-Seog Lee and the late M. S. Narasimhan, completed shortly before Narasimhan’s passing in 2021. This paper, which has already attracted wide attention in the research community, stands as a fitting tribute to his enduring influence in algebraic geometry.
